Compatibility of Drinfeld presentations for split affine Kac-Moody quantum symmetric pairs

Let (U, U^) be a split affine quantum symmetric pair of type Bₙ^ (1), Cₙ^ (1) or Dₙ^ (1). We prove factorization and coproduct formulae for the Drinfeld-Cartan operators ᵢ (z) in the Lu-Wang Drinfeld-type presentation, generalizing the type Aₙ^ (1) result from Prz23. As an application, we show that a boundary analogue of the q-character map, defined via the spectra of these operators, is compatible with the usual q-character map. As an auxiliary result, we also produce explicit reduced expressions for the fundamental weights in the extended affine Weyl groups of classical types.